Subgroups — C₁₉×#19897 #18025856

Order 4864.

638 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3392	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3387	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3278	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1705	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1631	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1623	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	—	2	1	no	—
17	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#557	C₂²	1	1	yes	characteristic
19	C₁₉×#550	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#501	—	2	1	no	—
22	C₁₉×#498	—	2	1	no	—
23	C₁₉×#498	C₂²	1	1	yes	characteristic
24	C₁₉×#498	C₂²	1	1	yes	characteristic
25	C₁₉×#498	C₂²	1	1	yes	characteristic
26	C₁₉×#492	—	2	1	no	—
27	C₁₉×#492	C₂²	1	1	yes	characteristic
28	C₁₉×#492	C₂²	1	1	yes	characteristic
29	C₁₉×#492	C₂²	1	1	yes	characteristic
30	C₁₉×#479	—	2	1	no	—
31	C₁₉×#477	C₂²	1	1	yes	characteristic
32	C₁₉×#476	—	2	1	no	—
33	C₁₉×#476	C₂²	1	1	yes	characteristic
34	C₁₉×#475	—	2	1	no	—
35	C₁₉×#475	—	2	1	no	—
36	C₁₉×#475	C₂²	1	1	yes	characteristic
37	C₁₉×#475	C₂²	1	1	yes	characteristic
38	C₁₉×#468	—	2	1	no	—
39	C₁₉×#462	C₂²	1	1	yes	characteristic
40	C₁₉×#461	—	2	1	no	—
41	C₁₉×#461	C₂²	1	1	yes	characteristic
42	C₁₉×#460	—	2	1	no	—
43	C₁₉×#460	C₂²	1	1	yes	characteristic
44	C₁₉×#460	C₂²	1	1	yes	characteristic
45	C₁₉×#452	—	2	1	no	—
46	C₁₉×#448	—	2	1	no	—
47	C₁₉×#446	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#441	—	2	1	no	—
51	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×SD₁₆×C₁₉	—	2	1	no	—
53	C₄×SD₁₆×C₁₉	—	2	1	no	—
54	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#436	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#333	C₂²	1	1	yes	characteristic
59	C₁₉×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₁₉	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	—	2	1	no	—
69	C₁₉×#137	—	4	4	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	—	2	1	no	—
79	C₂×SD₁₆×C₁₉	—	4	1	no	—
80	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₁₉	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	—	2	1	no	—
83	C₁₉×C₄⋊Q₈	—	2	1	no	—
84	C₁₉×C₄⋊Q₈	—	2	1	no	—
85	C₁₉×C₄⋊Q₈	—	2	1	no	—
86	C₁₉×C₄⋊Q₈	—	4	1	no	—
87	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₉×#127	—	2	1	no	—
91	C₁₉×#127	C₂³	1	1	yes	characteristic
92	C₁₉×#125	—	2	1	no	—
93	C₁₉×#125	—	4	1	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	4	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	4	1	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	—	2	1	no	—
101	C₄×Q₈×C₁₉	—	2	1	no	—
102	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#107	D₄	1	1	yes	characteristic
110	C₁₉×#106	—	2	1	no	—
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×#106	—	2	1	no	—
116	C₁₉×#106	—	2	1	no	—
117	C₁₉×#106	—	4	1	no	—
118	C₁₉×#106	D₄	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×C₄⋊C₈	—	2	1	no	—
121	C₁₉×C₄⋊C₈	—	2	1	no	—
122	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
125	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	2	1	no	—
131	C₁₉×#103	D₄	1	1	yes	characteristic
132	C₁₉×#103	D₄	1	1	yes	characteristic
133	C₁₉×#103	D₄	1	1	yes	characteristic
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	2	1	no	—
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×#97	—	2	1	no	—
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	#41×C₁₉	—	4	2	no	—
146	#41×C₁₉	—	8	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	4	1	no	—
151	C₂×Q₈×C₁₉	—	4	1	no	—
152	C₂×Q₈×C₁₉	—	4	2	no	—
153	C₂×Q₈×C₁₉	—	8	1	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	4	1	no	—
162	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	4	1	no	—
165	C₂²×C₄×C₁₉	—	4	1	no	—
166	Q₁₆×C₁₉	—	4	2	no	—
167	Q₁₆×C₁₉	SD₁₆	1	4	yes	complemented
168	SD₁₆×C₁₉	—	2	2	no	—
169	SD₁₆×C₁₉	—	4	2	no	—
170	SD₁₆×C₁₉	—	4	2	no	—
171	SD₁₆×C₁₉	—	4	2	no	—
172	SD₁₆×C₁₉	—	8	1	no	—
173	SD₁₆×C₁₉	—	8	1	no	—
174	SD₁₆×C₁₉	—	8	2	no	—
175	SD₁₆×C₁₉	—	8	1	no	—
176	SD₁₆×C₁₉	—	8	1	no	—
177	M₁₆×C₁₉	—	4	2	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	4	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	—	4	1	no	—
201	C₄⋊C₄×C₁₉	—	4	1	no	—
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	4	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₄²×C₁₉	—	2	1	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	4	1	no	—
213	C₄²×C₁₉	—	4	1	no	—
214	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
215	#19897	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	2	1	no	—
219	Q₈×C₁₉	—	2	1	no	—
220	Q₈×C₁₉	—	2	1	no	—
221	Q₈×C₁₉	—	2	1	no	—
222	Q₈×C₁₉	—	4	1	no	—
223	Q₈×C₁₉	—	4	1	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	Q₈×C₁₉	—	8	2	no	—
227	Q₈×C₁₉	—	8	1	no	—
228	Q₈×C₁₉	—	16	1	no	—
229	Q₈×C₁₉	C₂×SD₁₆	1	2	yes	—
230	Q₈×C₁₉	C₂×SD₁₆	1	2	yes	—
231	D₄×C₁₉	—	2	1	no	—
232	D₄×C₁₉	—	2	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	1	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	8	2	no	—
238	D₄×C₁₉	—	8	1	no	—
239	D₄×C₁₉	—	16	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	8	2	no	—
253	C₂×C₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
257	C₈×C₁₉	—	2	2	no	—
258	C₈×C₁₉	—	2	1	no	—
259	C₈×C₁₉	—	2	1	no	—
260	C₈×C₁₉	—	4	1	no	—
261	C₈×C₁₉	—	4	1	no	—
262	C₈×C₁₉	—	4	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	C₈×C₁₉	C₂×SD₁₆	1	2	yes	—
265	C₈×C₁₉	#137	1	2	yes	complemented
266	#3392	C₂×C₁₉	1	1	yes	characteristic
267	#3387	C₂×C₁₉	1	1	yes	characteristic, complemented
268	Q₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#3278	C₂×C₁₉	1	1	yes	characteristic
270	#1705	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1653	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1651	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1631	C₂×C₁₉	1	1	yes	characteristic
278	#1623	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1590	C₂×C₁₉	1	1	yes	characteristic, complemented
280	C₈×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	—	8	1	no	—
287	C₂²×C₁₉	D₄²	1	1	yes	characteristic
288	C₄×C₁₉	—	2	2	no	—
289	C₄×C₁₉	—	2	2	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	4	1	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	8	1	no	—
297	C₄×C₁₉	—	8	1	no	—
298	C₄×C₁₉	—	8	1	no	—
299	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
300	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
301	C₄×C₁₉	#577	1	1	yes	characteristic
302	C₄×C₁₉	#577	1	1	yes	characteristic
303	C₂×#137	—	2	1	no	—
304	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
305	#557	C₂²×C₁₉	1	1	yes	characteristic
306	#550	C₂²×C₁₉	1	1	yes	characteristic
307	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
308	#501	—	2	1	no	—
309	#498	—	2	1	no	—
310	#498	C₂²×C₁₉	1	1	yes	characteristic
311	#498	C₂²×C₁₉	1	1	yes	characteristic
312	#498	C₂²×C₁₉	1	1	yes	characteristic
313	#492	—	2	1	no	—
314	#492	C₂²×C₁₉	1	1	yes	characteristic
315	#492	C₂²×C₁₉	1	1	yes	characteristic
316	#492	C₂²×C₁₉	1	1	yes	characteristic
317	#479	—	2	1	no	—
318	#477	C₂²×C₁₉	1	1	yes	characteristic
319	#476	—	2	1	no	—
320	#476	C₂²×C₁₉	1	1	yes	characteristic
321	#475	—	2	1	no	—
322	#475	—	2	1	no	—
323	#475	C₂²×C₁₉	1	1	yes	characteristic
324	#475	C₂²×C₁₉	1	1	yes	characteristic
325	#468	—	2	1	no	—
326	#462	C₂²×C₁₉	1	1	yes	characteristic
327	#461	—	2	1	no	—
328	#461	C₂²×C₁₉	1	1	yes	characteristic
329	#460	—	2	1	no	—
330	#460	C₂²×C₁₉	1	1	yes	characteristic
331	#460	C₂²×C₁₉	1	1	yes	characteristic
332	#452	—	2	1	no	—
333	#448	—	2	1	no	—
334	#446	C₂²×C₁₉	1	1	yes	characteristic
335	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
337	#441	—	2	1	no	—
338	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
339	C₄×SD₁₆	—	2	1	no	—
340	C₄×SD₁₆	—	2	1	no	—
341	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
342	#436	C₂²×C₁₉	1	1	yes	characteristic
343	#335	C₂²×C₁₉	1	1	yes	characteristic
344	#334	C₂²×C₁₉	1	1	yes	characteristic
345	#333	C₂²×C₁₉	1	1	yes	characteristic
346	#332	C₂²×C₁₉	1	1	yes	characteristic
347	#332	C₂²×C₁₉	1	1	yes	characteristic
348	#331	C₂²×C₁₉	1	1	yes	characteristic
349	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
350	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
351	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
352	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
353	C₈²	C₂²×C₁₉	1	1	yes	characteristic
354	C₂×C₁₉	—	8	1	no	—
355	C₂×C₁₉	—	16	1	no	—
356	C₂×C₁₉	#3278	1	1	yes	characteristic
357	C₂×C₁₉	D₄×SD₁₆	1	1	yes	characteristic
358	C₂×C₁₉	#3291	1	1	yes	characteristic
359	C₂×#41	—	2	1	no	—
360	C₂²×Q₈	—	2	1	no	—
361	#137	—	4	4	no	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×SD₁₆	—	4	1	no	—
372	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
373	C₂×M₁₆	—	2	1	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	—	2	1	no	—
376	C₄⋊Q₈	—	2	1	no	—
377	C₄⋊Q₈	—	2	1	no	—
378	C₄⋊Q₈	—	4	1	no	—
379	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
382	#127	—	2	1	no	—
383	#127	C₂³×C₁₉	1	1	yes	characteristic
384	#125	—	2	1	no	—
385	#125	—	4	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	4	1	no	—
388	#121	—	2	1	no	—
389	#121	—	4	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
400	#107	—	2	1	no	—
401	#107	D₄×C₁₉	1	1	yes	characteristic
402	#106	—	2	1	no	—
403	#106	—	2	1	no	—
404	#106	—	2	1	no	—
405	#106	—	2	1	no	—
406	#106	—	2	1	no	—
407	#106	—	2	1	no	—
408	#106	—	2	1	no	—
409	#106	—	4	1	no	—
410	#106	D₄×C₁₉	1	1	yes	characteristic
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	—	2	1	no	—
414	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
418	#103	—	2	1	no	—
419	#103	—	2	1	no	—
420	#103	—	2	1	no	—
421	#103	—	2	1	no	—
422	#103	—	2	1	no	—
423	#103	D₄×C₁₉	1	1	yes	characteristic
424	#103	D₄×C₁₉	1	1	yes	characteristic
425	#103	D₄×C₁₉	1	1	yes	characteristic
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	D₄×C₁₉	1	1	yes	characteristic
430	C₂²⋊C₈	—	2	1	no	—
431	#97	—	2	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	—	2	1	no	—
434	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
437	C₁₉	#19897	1	1	yes	characteristic, direct product factor, Sylow
438	#41	—	4	2	no	—
439	#41	—	8	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	4	1	no	—
444	C₂×Q₈	—	4	1	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	—	8	1	no	—
447	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	Q₁₆	—	4	2	no	—
460	Q₁₆	SD₁₆×C₁₉	1	4	yes	complemented
461	SD₁₆	—	2	2	no	—
462	SD₁₆	—	4	2	no	—
463	SD₁₆	—	4	2	no	—
464	SD₁₆	—	4	2	no	—
465	SD₁₆	—	8	1	no	—
466	SD₁₆	—	8	1	no	—
467	SD₁₆	—	8	2	no	—
468	SD₁₆	—	8	1	no	—
469	SD₁₆	—	8	1	no	—
470	M₁₆	—	4	2	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	4	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
508	C₂³	—	2	1	no	—
509	C₂³	—	4	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	8	2	no	—
519	Q₈	—	8	1	no	—
520	Q₈	—	16	1	no	—
521	Q₈	C₂×SD₁₆×C₁₉	1	2	yes	—
522	Q₈	C₂×SD₁₆×C₁₉	1	2	yes	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	8	2	no	—
530	D₄	—	8	1	no	—
531	D₄	—	16	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
548	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
549	C₈	—	2	2	no	—
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	C₂×SD₁₆×C₁₉	1	2	yes	—
557	C₈	C₁₉×#137	1	2	yes	complemented
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	D₄²×C₁₉	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
577	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
578	C₄	C₁₉×#577	1	1	yes	characteristic
579	C₄	C₁₉×#577	1	1	yes	characteristic
580	C₂	—	8	1	no	—
581	C₂	—	16	1	no	—
582	C₂	C₁₉×#3278	1	1	yes	characteristic
583	C₂	D₄×SD₁₆×C₁₉	1	1	yes	characteristic
584	C₂	C₁₉×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#550	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₉×#3387	C₂	semidirect
3. Q₈×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1705	C₂	semidirect
6. C₁₉×#1691	C₂	semidirect
7. C₁₉×#1686	C₂	semidirect
8. C₁₉×#1672	C₂	semidirect
9. C₁₉×#1666	C₂	semidirect
10. C₁₉×#1653	C₂	semidirect
11. C₁₉×#1651	C₂	semidirect
13. C₁₉×#1623	C₂	semidirect
14. C₁₉×#1590	C₂	semidirect
15. C₈×Q₁₆×C₁₉	C₂	semidirect
167. Q₁₆×C₁₉	SD₁₆	semidirect
215. #19897	C₁₉	direct (N × H)
265. C₈×C₁₉	#137	semidirect
267. #3387	C₂×C₁₉	semidirect
268. Q₈×SD₁₆	C₂×C₁₉	semidirect
270. #1705	C₂×C₁₉	semidirect
271. #1691	C₂×C₁₉	semidirect
272. #1686	C₂×C₁₉	semidirect
273. #1672	C₂×C₁₉	semidirect
274. #1666	C₂×C₁₉	semidirect
275. #1653	C₂×C₁₉	semidirect
276. #1651	C₂×C₁₉	semidirect
278. #1623	C₂×C₁₉	semidirect
279. #1590	C₂×C₁₉	semidirect
280. C₈×Q₁₆	C₂×C₁₉	semidirect
437. C₁₉	#19897	direct (N × H)
460. Q₁₆	SD₁₆×C₁₉	semidirect
557. C₈	C₁₉×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3392	2
C₁₉×#3387	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3278	2
C₁₉×#1705	2
C₁₉×#1691	2
C₁₉×#1686	2
C₁₉×#1672	2
C₁₉×#1666	2
C₁₉×#1653	2
C₁₉×#1651	2
C₁₉×#1631	2
C₁₉×#1623	2
C₁₉×#1590	2
C₈×Q₁₆×C₁₉	2
#19897	19

Subgroups — C19×#19897 #18025856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19897 #18025856